Let a and b be real numbers with a < b. Let f : (a, b) → R be Score: /25 points an increasing function. Suppose that f has the intermediate value property: if a < c < d < b and f(c) < τ < f(d), then there is a real number t with c < t < d and with f(t) = τ . Let x ∈ (a, b). Prove that f is continuous at x.